I recognize that the existing answer, apart of the fact that it is written in French, might also be a little too abstract for immediate needs.

First of all, a general thumb rule is that epithet adjectives go after the noun, unless this adjective is frequently used ("small words") or an idiom, in which case a rule of Old French applies (the adjective goes before the noun).

In general:

Un chapeau élégant

But:

Un beau chapeau

(small and frequent word).

In general:

Un homme grand

(the man is tall), but:

Un grand homme

is an idiom (meaning famous, briliant, etc.)

There is nothing mysterious there, but we will see that it does have an impact on the order.

Here is the rule of thumb: the closest the adjective is related to the noun (modifies it), the closest it should be in the sentence. That sounds quite sensible: considering that in French you first hear a noun and then its modifiers, the message will come across better if the first ones go first.

While linguists will go into disquisitions about whether there are rules of what is generally considered more modifying (or whether there could be rules at all), I guess you can go a long way with your common sense and some observation.

Let’s see a few examples:

If you use the colors "vert" and "foncé", obviously "vert" is more "modifying" (for your purposes) than "foncé", hence:

Un chapeau vert foncé

When you have more than two, it becomes unwieldy anyway, so you might have to articulate with commas and coordination conjunctions:

Un chapeau chaud et/mais vert foncé,

… the order now depending on what you want to say (it’s obvious, however that the color "foncé" should stick with "vert").

But since color can be judged less important than warmth (at least in cold weather), a Cartesian discussion partner might start wondering why "chaud" is coming as an afterthought. You should prepare to justify yourself:

Un chapeau vert foncé, également chaud

Un chapeau vert foncé, d’ailleurs chaud

And what if we use beau/élégant on top of it? It depends again on what you want to stress:

Un chapeau élégant, chaud et vert foncé,

It starts looking like a good, proper and idiomatic advertisement (in which case aesthetics might be more important than warmth). On the other hand, since "beau" conventionally goes before the noun:

Un beau chapeau, chaud et vert foncé,

But if you want to sound quaint, you could also go "traditional order" with the word "elegant" and throw it in front of the noun:

Un élégant chapeau, chaud et vert foncé,

But unless you are auctioning the hat at Christie’s, and especially when you sell on Ebay, you might want to stay with "chapeau élégant".

These are rules of thumb, but it could take you a long way.